It's a US-spec final-year F1. These were called the "S" model by Berliner (but not by Ducati SpA). These were all built in 1987 but many weren't sold/titled until 1988. I have an F1-S much like this one but mine is titled as a 1988 Cagiva! These are the only F1's that were ever sold as street-legal bikes in the US.

The dual exhaust is wretched, it must weigh 40 pounds and should be the first thing you remove. The canonical replacement is a Verlicchi open reverse megaphone. I have done this and can give you jetting info for 36mm carbs.